When light strikes a mirror, it undergoes reflection. The incident light ray makes an angle of incidence (i) with the normal (a line perpendicular to the surface) at the point of incidence. The reflected light ray makes the same angle of reflection (r) with the normal on the opposite side of the incident ray.

According to the law of reflection, the angle of incidence is equal to the angle of reflection:

```

i = r

```

Refraction by a Hand Lens:

When the reflected light from the mirror strikes a hand lens (assuming it's a converging lens), it undergoes refraction. As light passes from air into a denser medium (in this case, the glass of the lens), it bends towards the normal. This bending of light is known as refraction.

At the point of incidence, the incident light ray makes an angle of incidence (i1) with the normal to the surface of the lens. The refracted light ray bends towards the normal and makes an angle of refraction (r1) with the normal.

According to Snell's law of refraction, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for a given pair of media. This constant ratio is known as the refractive index (n) of the denser medium:

```

n = sin i1 / sin r1

```

After refraction through the hand lens, the light rays converge towards a point called the focal point (F) of the lens. The distance between the lens and the focal point is known as the focal length (f).

The path of light after striking the mirror and then the hand lens can be summarized as follows:

1. The incident light strikes the mirror and reflects off it, obeying the law of reflection (i = r).

2. The reflected light travels towards the hand lens.

3. As the reflected light strikes the hand lens, it refracts towards the normal due to the change in medium from air to glass.

4. The refracted light rays converge towards the focal point (F) of the hand lens.

This is a basic description of what happens to the path of light after it strikes a mirror and then a hand lens. The exact behavior of light depends on the specific properties and geometry of the mirror, hand lens, and incident light.